Local convergence analysis of inexact Gauss–Newton like methods under majorant condition

Abstract

In this paper, we present a local convergence analysis of inexact Gauss–Newton like methods for solving nonlinear least squares problems. Under the hypothesis that the derivative of the function associated with the least squares problem satisfies a majorant condition, we obtain that the method is well-defined and converges. Our analysis provides a clear relationship between the majorant function and the function associated with the least squares problem. It also allows us to obtain an estimate of convergence ball for inexact Gauss–Newton like methods and some important, special cases.